Normal families on sequence of omitted functions
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摘要: 设~$\{f_{n}\}$~是区域~$D$~内的亚纯函数列,~其零点的重级均~$\geq3$, 且均仅有一个重级极点. ~$\{h_{n}\}$~是~$D$~内的亚纯函数列,~且~$h_{n}\Rightarrow h$~于~$D$, $h \not \equiv \infty,h \ne 0$. 若~$f'_{n}\ne h_{n}$, 则~$\{f_{n}\}$~在~$D$~内正规.Abstract: Let~$\{f_{n}\}$~be a sequence of meromorphic functions on a domain~$D$,~all of whose zeros have multiplicity at least $ 3$,and each of which has a multiple pole. Let $\{h_{n}\}$~be a sequence of meromorphic functions on~$D$, such that~$\{h_{n}\}$~converges spherically locally uniformly to a function~$h$ which is meromorphic and zero-free on $D$. If~$f'_{n}\ne h_{n}$, then~$\{f_{n}\}$~is normal on~$D$.
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Key words:
- meromorphic function /
- normal family /
- sequence of omitted functions
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